Abstract
We introduce the notion T does not omit obstructions. If a stable theory does not admit obstructions then it does not have the finite cover property (nfcp). For any theory T, form a new theory $T_{\rm Aut}$ by adding a new unary function symbol and axioms asserting it is an automorphism. The main result of the paper asserts the following: If T is a stable theory, T does not admit obstructions if and only if $T_{\rm Aut}$ has a model companion. The proof involves some interesting new consequences of the nfcp.
Citation
John T. Baldwin. Saharon Shelah. "Model Companions of $T_{\rm Aut}$ for Stable T." Notre Dame J. Formal Logic 42 (3) 129 - 142, 2001. https://doi.org/10.1305/ndjfl/1063372196
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